A survey of the Path Partition Conjecture
Marietjie Frick · Discussiones Mathematicae Graph Theory · 2013
The Path Partition Conjecture (PPC) states that if G is any graph and (λ 1 , λ 2 ) any pair of positive integers such that G has no path with more than λ 1 + λ 2 vertices, then there exists a partition (V 1 , V 2 ) of the vertex set of G such that V i has no path with more than λ i vertices, i = 1, 2. We present a brief history of the PPC, discuss its relation to other conjectures and survey results on the PPC that have appeared in the literature since its first formulation in 1981.